Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint/idempotentHint/non-destructive, so safety is covered. The description's only added behavior claim is the return shape {common_difference, nth_term, sum_of_n}, which duplicates the output schema and adds little beyond structured data.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Two short sentences with the core computation front-loaded and no filler. The trailing list_bundles pointer is mildly tangential to invocation but is a legitimate navigation aid, keeping it just short of ideal.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With an output schema present and full parameter coverage, the description need not explain return values or inputs. It covers the core purpose adequately; only explicit routing guidance among the many math siblings is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100% and each of the four parameters is documented in-schema (including the arithmetic/geometric enum). The description adds no syntax or format detail beyond what the schema already provides, so the baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource: computing the nth term and sum of an arithmetic or geometric sequence. That scope is unambiguous and clearly separable from the hundreds of other calculate_* siblings, which cover unrelated domains.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is implied by the stated computation, and the description points to list_bundles for related 'math' calculators, which is a discovery hint rather than tool-selection guidance. It never says when to prefer this over calculate_equation or calculate_factorial_permutation, nor any prerequisites.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.